2011/10/31 by Cédric M. Campos, Elisa Guzmán, E Guzmán +1 · 14 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Euler's formula #Euler–Lagrange equation #Fibration #First order #Formalism (music) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hamiltonian (control theory) #Lagrangian #Manifold (fluid mechanics) #Mathematical analysis #Mathematical optimization #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Pure mathematics #math-ph #math.DG #math.MP #msc:53D12 #msc:70H03 #msc:70H05 #msc:70S05
paper · pdf · doi:10.3934/jgm.2012.4.1
published in The Journal of Geometric Mechanics 4(1), 1-26 (American Institute of Mathematical Sciences) · preprint, 27 pages
arxiv created 2011/12/05 · openalex publication_date 2012/01/01 · arxiv updated 2015/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A description of classical field theories of first order in terms of Lagrangian submanifolds of premultisymplectic manifolds is presented. For this purpose, a Tulczyjew's triple associated with a fibration is discussed. The triple is adapted to the extended Hamiltonian formalism. Using this triple, we prove that Euler-Lagrange and Hamilton-De Donder-Weyl equations are the local equations defining Lagrangian submanifolds of a premultisymplectic manifold.